The displacement of two sinusoidal waves is given by the equations:
$y_1 = 8 \sin(20x - 30t)$
$y_2 = 8 \sin(25x - 40t)$
Then the phase difference between the waves at time $t = 2 \ s$ and distance $x = 5 \ cm$ will be:

$A$ wave travelling in the $-z$ direction having displacement along the $x$ direction as $1 \ m$,wavelength $\pi \ m$,and frequency $\frac{1}{\pi} \ Hz$ is represented by:

If the frequency of a wave is increased by $25 \%$,then the change in its wavelength is (medium not changed).

$A$ transverse sinusoidal wave moves along a string in the positive $x$-direction at a speed of $10 \text{ cm/s}$. The wavelength of the wave is $0.5 \text{ m}$ and its amplitude is $10 \text{ cm}$. At a particular time $t$,the snapshot of the wave is shown in the figure. The velocity of point $P$ when its displacement is $5 \text{ cm}$ is:

For the harmonic travelling wave $y = 5 \cos 2\pi (10t - 0.008x + 3.5)$ where $x$ and $y$ are in $cm$ and $t$ is in seconds. What is the phase difference between the oscillatory motion at two points separated by a distance of:
$(a)$ $4 \ m$
$(b)$ $0.5 \ m$
$(c)$ $\frac{\lambda}{2}$
$(d)$ $\frac{3\lambda}{4}$ (at a given instant of time)
$(e)$ What is the phase difference between the oscillation of a particle located at $x = 100 \ cm$,at $t = T \ s$ and $t = 5 \ s$?

Write the equation of displacement of an element of a medium in a harmonic wave.